Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C27×C4 |
| direct product | C19×#34197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(25,28)(29,31)(33,34)(36,44)(38,40)(42,47);(32,33,37,34)(35,40,43,38)(36,39,44,41)(42,46,47,45);(24,25)(26,29)(27,28)(30,31)(32,34,37,33)(35,40,43,38)(36,41,44,39)(42,46,47,45);(32,35,37,43)(33,38,34,40)(36,42,44,47)(39,45,41,46);(24,26,27,30)(25,29,28,31)(32,36)(33,39)(34,41)(35,42)(37,44)(38,45)(40,46)(43,47)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27185);